1. Field of the Invention
The invention relates to a method for digitally producing contour lines from height points above a polygon net.
2. Background and Related Art
Methods of this type are carried out, for example, by a computer system for the purpose of image processing. The aim of the method is to calculate, in the case of an uneven surface formed by the height points, the lines of the same height and display them, for example, on an image screen. This is comparable to a geographic map on which the lines of the same height are drawn for a landscape consisting of mountains and valleys.
When calculating contour lines of this type, a particular problem arises with so-called saddle surfaces, which are produced, for example, by a square sheet of paper being bent up at two mutually diagonal corners and bent down at the other two diagonal corners. A so-called saddle point, which is uninfluenced by the bends, remains approximately in the centre of the paper.
To produce contour lines, it is necessary for a plane of the desired height to intersect the saddle surface. If this intersecting plane is situated above the saddle point, the bent-up corners of the paper are intersected. If, however, the intersecting plane is situated below the saddle point, the bent-down corners of the paper are intersected. Completely different contour lines are obtained depending upon whether the bent-up or the bent-down corners of the paper are intersected. In the present example, the contour lines assigned to the bent-up corners are arranged approximately at right angles to the contour lines assigned to the bent-down corners.
Because of the enormous computation work involved, inter alia, a computer system does not normally calculate the entire contour lines of the saddle surface. Instead, the computer system calculates the intersections of the connecting lines, limiting the saddle surface, with the desired intersecting plane. This calculation results in four intersections, of which in each case two neighbouring intersections must be connected to form a contour line. The contour lines are obtained above the saddle point in the case of one intersecting surface and below the saddle point in the case of one intersecting surface, depending upon which neighbouring intersections are interconnected.
The decision as to which of the possible contour lines are the correct ones in the particular case is usually made by means of so-called path-tracing algorithms, in which the computer system considers the polygons made up of the individual contour lines as a whole. It has emerged that path-tracing algorithms of this type are not error-free and that changes in the polygon net on which the entire calculations are based also lead to errors.